Tilburg University
Diffusion, uncertainty and firm size
Nooteboom, B.
Published in:
International Journal of Research in Marketing
Publication date:
1989
Link to publication
Citation for published version (APA):
Nooteboom, B. (1989). Diffusion, uncertainty and firm size. International Journal of Research in Marketing, 6,
109-128.
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109
Diffusion, uncertainty and firm size
Bart NOOTEBOOM *
Studies of the role of small vs. large firms in innovation go
back to Schumpeter. In studies of product innovation, recent
literature points to a ‘dynamic complementarity’ between small
and large firms. In studies of the adoption of (process) innovations (diffusion), the effect of firm size has been studied much
less. David (1975) and Davies (1979) proposed models which
hinge on some ‘critical firm size’ beyond which adoption takes
place. In these models, risk is not treated explicitly. In the
theory of capital investment decisions, adoption is generally
treated as a determinate decision based on a trade-off between
expected returns and risk.
The present paper presents an alternative model, inspired by
the ‘behavioral theory’ school of economic theory. The decision to adopt is treated as a gamble with odds in favour
depending on expected returns and odds against depending on
risk. Under reasonable side-assumptions, expected returns are
proportional to size and risk is independent of size. This yields
a probability of adoption which depends on firm size without
any ‘critical firm size’. The model is tested and estimated on
data concerning the diffusion of general purpose computers in
the Netherlands.
The paper closes with a discussion of further research and
implications for industrial marketing and for technology policy.
1. Introduction
According to Rosenberg (1982, p. 106) the
study of technological innovation consists of
a series of footnotes to Schumpeter.’ But
concerning the role of small firms in comparison with large firms, Schumpeter’s work, when
considered as a whole, is ambivalent. In his
earlier work (“Theory of economic development and business cycles”), Schumpeter proposed the view that innovations are generated
* Author’s address: Department of Business Administration,
University of Groningen, Landleven 5, P.O. Box 800, 9700
AV Groningen, The Netherlands.
’ Brouwer (1986, p. 749).
Intern. J. of Research in Marketing 6 (1989) 109-128
North-Holland
0167-8116/89/$3.50
by new, small firms. Later (in Schumpeter’s
“Capitalism, socialism and democracy”) this
was replaced by the view that innovations are
generated more by established, large firms
with monopoly power, since only they can
command the resources for research and development. Surveys of later work, presented
b y Scherer (1980), K a m i e n a n d Schwarz
(1982) and Stoneman (1983) indicate that
Rosenberg’s general characterization is largely
correct, in the sense that the opposition between the ‘small firm’ and ‘large firm’ theses
is still unresolved.2 The issue is too complex
to allow for a single sweeping statement concerning the relation between innovation and
firm size, regardless of types and conditions
of innovation. It is plausible and there are
empirical indications (see, e.g., Rothwell and
Zegveld, 1982; Nooteboom, 1984), that the
generation of fundamentally new ‘high technologies’ (cf.’ Rosegger, 1980), shifting ‘stateof-the-art’ boundaries, prior to applications,
and complex large scale applications are the
province of large firms (or joint ventures or
large firms), while applications in novel product/market combinations, product adaptation and product/service combinations are
the province of smaller firms. The reasons for
this are straightforward: The first class of
innovations requires large teams of highly
specialized labour and large capital outlays
and carries great risks, which only large firms
or joint ventures between them can sustain.
The second class of innovations requires close
interaction with customers and a type of reckless unorthodoxy and flexibility that provides
scope for small entrepreneurs.
2 It would not be very useful, and would consume too much
space to repeat the surveys in the present paper.
0 1989, Elsevier Science Publishers B.V. (North-Holland)
110
B. Nooleboom
/ Diffusion, uncertainly and firm size
As formulated by Rothwell (1985, p. 9):
the advantages of large firms are material and
those of small firms behavioral. From this,
the notion emerges of a certain ‘dynamic
complementarity’ between small and large
firms, where small and medium sized enterprises ‘play different roles at different periods of time in different industries’.3 According to the complementarity hypothesis, the
different roles of small and large business 4 in
the course of the life cycle of a product (or
product class) are as follows: generation of
new basic technology: large firms (and universities); daring implementation in new
product/market combinations: small and
medium sized firms; large scale, efficient production and distribution: large firms (often
after take-overs of succesful small innovator
firms); adaptations for specialized or residual
market niches in the maturity phase of the
product: small firms (often in the form of
product/service combinations).5
This complementarity view of small and
large business is gaining acceptance as the
basis for technology policy, aimed at removing obstacles in the access of small and
medium sized firms to information/knowledge and finance, to let them play their role.6
Implicitly or explicitly, most innovation studSee Rothwell and Zegveld (1982, p. 245).
the statistical demarcation of small and medium sized business varies (between different countries and different agencies/institutions within countries) from less than 100 people
engaged, to less than 500 or even (many) more people
engaged. In manufacturing 100 people is perhaps too low but
a boundary much higher than 500 people is not very useful.
The notion of complementarity should not be carried so far
as to suggest that there is no competition or conflict between
large and small business. Complementarity arises mainly on
the macro level of the generation and diffusion of innovations. It may also arise on the micro level, in the form of
relations of comakership or joint R&D, but it may also go
together with fierce competition on the micro level, with
small firms challenging large firms in the early phase, small
firms being pushed out of the market or being taken over by
large firms in the phase of growth, and small ,firms being
kept out of the market in the consolidation phase.
Cf. Rothwell and Dodgson (1987) Dekker Committee (1987),
and WRR (1987).
ies concentrate on the development and introduction to the market of new products. Some
of these products are means of production
(materials, processes, methods and tools). An
important issue is the adoption (diffusion) of
these process innovations, and differences in
this area between small and large firms. That
is the subject of the present paper. Empirical
evidence indicates that small firms are systematically lagging behind in the adoption of
process innovations developed by other firms,
and the question to be considered here is how
this is to be explained.7
2. Diffusion and firm size in the literature
In the economics literature, Stoneman
(1983) classifies studies of diffusion into three
types: intrafirm, intra-sectoral and economy
wide. Reviewing the state of the art in intrasectoral studies of diffusion, he discusses
the psychological approach, the probit approach and the game theoretic approach. He
further identifies four questions for studies of
diffusion:
(1) what determines the post-diffusion
(saturation) level of use or ownership?
(2) why are some users early and others
late?
(3) what time path will use follow and
why?
(4) what characteristics of (potential) users
are the key factors in influencing that time
path?
We add two further questions:
(5) how does use depend on firm size (in
the case of process innovations), and why?
(6) how is the decision to adopt taken in
view of uncertainty?
’ Empirical evidence on the lag of small firms in the introduction of automation (both general purpose computers and
process automation), for example, is given in official statistics and surveys by commercial market research firms (in the
Netherlands: the Central Bureau of Statistics and NIPO).
B. Nooteboom / Diffusion, uncertainty and firm size
According to the ‘psychological approach’
(a term attributed to David, 1969), “diffusion
takes time because actors respond to stimuli
only with a lag, and these lags differ across
the population”.8 Much work in this area has
been conducted by Mansfield (1968), on the
basis of the epidemic or contagion model,
yielding a logistic diffusion curve, with profitability and size of the investment as determinants of the speed of diffusion. In his study
of the diffusion of computers, Chow (1967)
also used the contagion model, but found the
Compertz specification to be preferable to the
logistic, and included an effect of the price
decline of computers on the saturation level
of demand. Similar extensions/modifications
with respect to the logistic curve have also
been studied.’ Firm size and decision-making
under uncertainty (questions (5) and (6)) are
not modelled explicitly. In the game-theoretic
approach (Reinganum, 1981) information is
assumed to be perfect, firms are assumed to
be identical and different adoption dates are
derived from a Nash equilibrium in an
oligopoly game. Here also, firm size and uncertainty are not included in the analysis.
The probit approach focuses on the characteristics of individuals in the sector and
yields results as to which firms are early
adopters and which late, and yields results on
the effect of firm size. In particular, David
(1969, 1975) and Davies (1979) developed
models of the ‘critical level’ type: when some
stimulus variate takes on a value exceeding a
critical level, the subject of stimulation responds by instantly determining to adopt the
innovation in question.” Different subjects
adopt at different times because either the
stimulus variate or the critical level is subject
to a distribution of values, rather than a
unique value for all subjects. If S is the
stimulus variate, with relative density func8 Stoneman (1983, p. 93).
9 See, for example, Wahlbin (1982).
lo Stoneman (1983, p. 109).
111
tion f(S), and S*(t) is the critical value at
time C, then the proportion of adopters at
time t is given as
wf(S) dS.
Js*
(1)
David and Davies both take firm size as
the central variable (S), and consider how
firm size is distributed within the sector and
how the critical or threshold value of firm size
is determined. David’s (1975) hypothesis is
that critical size S *(t ) is defined by the point
where labour savings due to adoption (assumed to be proportional to size) equal the
cost of installing the innovation (assumed to
be independent of size). Assuming exponential growth of the wage rate relative to the
cost of the innovation, yielding an exponential decline of critical size, and assuming a
constant lognormal distribution of firm size,
David arrives at a time path of diffusion in
the form of a cumulative normal distribution.”
As noted by Davies (1979), a limitation of
David’s model is that it hinges on the ‘lumpiness’ of the investment: if both costs and
benefits are strictly porportional to firm size,
the effect of firm size disappears.12 The hypothesis developed by Davies (1979) is that a
firm will use a new technology if the expected
pay-off period is less than some critical period,
while both the expected and critical pay-off
periods are functions of firm size and other
firm characteristics. This yields the following
ownership condition: adoption by firm i of
size S(it) occurs if it exceeds some critical
size S * (it), where this critical size is proportional to the product of a large number of
firm characteristics. Assuming independence
of these characteristics an appeal to the central
limit theorem yields a lognormal distribution
of critical size. This yields a functional relationship between firm size and the probability
” David (1969).
‘* Davies (1979, p. 31).
112
B. Nooreboom / D i f f u s i o n , u n c e r t a i n t y a n d f i r m s i z e
of adoption according to a cumulative
lognormal curve. The procedure for arriving
at this curve is adopted from earlier studies of
the diffusion of consumer durables, yielding a
cumulative lognormal ‘Quasi Engel curve’.
The aggregate diffusion curve is now found
by aggregating the curve over the size distribution of firms. Using two alternative specifications of the dependency of critical size upon
time, for two different classes of innovation,
and assuming a lognormal size distribution,
Davies arrives at a time path of diffusion
according to a cumulative normal or a cumulative lognormal distribution.
The structure of Davies’ model is in fact
very similar to that of David’s model: both
models employ critical size, beyond which
adoption is certain, and there is no consideration of uncertainty, risk or lack of information in the adoption decision. The main difference (apart from the considerations yielding a critical size) is that Davies attaches a
lognormal variate to critical size, on the assumption that the factors determining critical
size, in terms of firm characteristics, are many
and independent. Those factors are said to
include “ technical attributes [ . . _] such as the
nature of its (the firm’s) products, existing
processes and inputs [ . . . ] and [ _ _. ] other
attributes such as educational attainment of
managers and research intensity [ . . . ] age of
management, degree of internal financing,
profit trends, growth performance and other
variables influencing attitudes to risk”.i3 In
fact, studies of small business and their
markets indicate that the independence of
these attributes from each other and from
firm size is questionable, to say the least, and
thereby the assumption of a lognormal variate
is subject to criticism.
Summing up, different studies of diffusion
address parts of the issue which all seem
relevant: psychological lags in response, prof-
I3 Davies (1979, pp. 68-70).
itability, size and lumpiness of investment,
preemptive or retaliatory actions of competitors, time required to recover costs of investment, firm characteristics, relative price of the
investment. The effect of firm size hinges on
the notion of critical size. Risk is mentioned
as a factor in the decision to adopt, but is not
treated explicitly in a trade-off with expected
profitability. There appear to be no studies
which take all relevant factors into account
simultaneously, presumably because that
would no longer yield a model which is analytically elegant and tractable. Perhaps requisite complexity should be preferred, at the
cost of surrendering analytical tractability,
which would lead research further along the
path of simulation as pioneered, in this area,
by Ijiri and Simon (1977) and Nelson and
Winter (1974, 1982). Nevertheless, the present
paper makes another attempt at an analytical
model, with the following focus: adequate
treatment of uncertainty in the decision to
adopt and of the effect of firm size.
In the marketing literature, a survey of
diffusion research has been edited by Mahajan and Wind (1986). The basis is formed by
the work of Fourt and Woodlock (1960), Bass
(1969), and the work by Mansfield mentioned
before. The Bass model is an additive combination of the Logistic model, where the increase of adopters depends on the interaction
of potential and actual adopters (imitation
effect), and the Fourt-Woodlock model,
where the increase depends only on the number of potential adopters (innovator effect).
Part of later research was aimed at more
general and more flexible diffusion functions.
An important line of research for marketing
has been the incorporation in the model of
marketing mix variables such as price and
promotion (for a review, see Kalish and Sen,
1986), and competition against existing and
potential firms.
Dolan, Jeuland and Muller ’ (1986) and
Eliashberg and Chatterjee (1986) indicated in
their review that stochastic considerations, to
B. Nooteboom
/ Diffusion, uncertainty and firm size
deal with uncertainty, are not well developed.
They report Markov-chain models of transition probabilities between stages in the buying process, which incorporate bayesian learning (derived from the economics literature)
and Von Neumann-Morgenstern utility.
Chatterjee and Eliashberg themselves are
working on a model of the adoption process
on the basis of a random walk over pieces of
information. Apart from this latter work,
models of the decision process which take
into account uncertainty appear to be scarce.
What work there is, appears to concentrate
on adoption decisions by consumers. Work
on decisions to adopt process innovations
which adequately deals with uncertainty and
takes into account the effect of the firm size
of adopters does not appear to be available.
3. Decisions under uncertainty
Clearly, the adoption of an innovation entails uncertainty: are expectations (promises
from suppliers) concerning cost saving or quality improvement realistic; what unforeseen
hitches will arise in adaptations of the innovation to the operating conditions of the
firm, or vice versa, adjustments of the firm to
the innovation (complementary investments,
training, organisation,
acceptance,
procedures)? The crucial question seems to be: how
much spending may be required, and for how
long, to bring performance up to standards/
expectations. And the bottom line: what
chance is there that in the end the balance of
costs and benefits is negative, in which case
adoption should not take place? As the innovation matures, risk in terms of the gap
between what is expected and what might
happen is reduced. Next to improvements in
cost/benefit properties, as the innovation matures, this may be the main determinant of
diffusion. Clearly, the relevant category is
perceived risk, which may decline because
more information is available or because in-
113
formation is diffused more widely and/or is
perceived to be more reliable (more colleagues with hands-on experience). This links
up with contagion models but with the precise interpretation of reducing risk. Thus the
decision to adopt is a two sided issue: expected net present value (NPV) of savings or
enhanced revenues on one side, and (perceived) probability of negative net present
value (risk) on the other side. NPV and its
perceived variance will in general depend on
firm characteristics such as: firm size (economies of scale, spread and thereby mutual
compensation of risks), expected pre-emptive
or retaliatory activities of competitors (with
possible asymmetries with respect to firm
size), age and educational level of entrepeneurs or staff (correlated with type of
product and firm size), degree of risk aversion, time preference of returns as expressed
in a discount rate.
Summing up: particularly in the area of
innovation it would be descriptively false,
normatively wrong and scientifically unfruitful to disregard risk in adoption decisions.i4
To proceed, the central question now is
how the trade-off between expected returns
and risk of failure is to be represented. It
would be wrong to incorporate risk by adding
a risk premium to the discount rate for NPV
calculations. The fault in this is that time
preference and risk preference are conflated,
with the result that risk introduces a systematic bias in favour of short term returns.
Under the assumption of rational and perfect financial markets, in the sense that the
shareholder’s interest prevails and full information on expected returns and risks of all
investment opportunities is available, the decision rule is as follows: invest in an internal
I4
Descriptively false: in fact, entrepreneurs are sensitive to
risk, next to expected or possible rewards; normatively
wrong: it would not be in the interest of the firm to
recommend decisions on the basis of expected returns only;
scientifically unfruitful: reduction of risk in time is likely to
be a major determinant of diffusion.
114
B. Nooteboom
/ Diffusion, uncertainty and firm size
project if its NPV is higher than that of a
package of traded securities with the same
level of risk. There are two problems in this
approach. The first problem is that it may be
rational even from the shareholders point of
view to prefer internal investment opportunities to external investment in traded securities, even if its NPV is lower, for strategic
reasons: to establish a basis for future profits,
or to provide for a spreading of risks or for
flexibility. These aspects are labelled‘options’
by Myers (1987, p. 12), who indicates that
methods are being developed to incorporate
the value of such options in calculations of
evaluation that will be solved. The second
problem is more fundamental: shareholders’
interest may not prevail, and internal investment opportunities are preferred to pay-out
of dividends or external investments in securities in order to achieve economically unorthodox objectives of management (growth,
market share, number of staff, personal
power).i5 The power of management to do so
is plausible in view of the first problem:
knowing that for strategic reasons internal
projects with relatively low NPV may be warranted, it is difficult for shareholders to distinguish legitimate cases from managerial objectives dressed up as strategic options. In
fact, management itself may not be able to
make the distinction, since strategic evaluations will inevitably be coloured by subjective
evaluations and personal views and ambitions. However the normative side of this
issue may turn out, descriptively it seems
realistic to concentrate on the process of
managerial choice from a set of internal investment opportunities. Since different internal alternatives seldom have the same level of
risk, the problem now is how expected returns
and risk are traded off in the selection of
investment projects.
l5 Cf. Marris and Wood (1971).
cc
T
li
in
A
----.-.A
Z
I+++
Fig. 1.
There is a considerable body of literature
on decisionmaking under uncertainty.16 A
prominent line in this is the approach attributed to Markowitz (1970) on the basis of
indifference curves in an expected value (p)
standard deviation (a) plane.”
The basic principle is illustrated in Fig. 1.
The optimal investment opportunity lies
where an indifference curve I(i) is tangent to
the set of investment opportunities A. Z is
the corresponding ‘certainty equivalent’: The
certain (u = 0) revenue an entrepeneur would
trade for the investment opportunities with
higher expected returns (p) and higher risks
((J) along the indifference curve. The difference in expected return between an investment opportunity and the corresponding certainty equivalent (n) is the ‘subjective price
of risk’ at that level of risk (a).
Investment occurs if there is at least one
opportunity on an indifference curve with a
certainty equivalent exceeding the return on a
risk free asset (such as a government bond).
Investment behavior varies primarily due to
differences in the subjective pricing of risk.
A minor point of critisism is that it is not
the standard deviation (a) that counts, but
the probability that net present value falls
below some minimum acceptable level (typically zero, but possibly some other level, below which the firm would go bankrupt). The
\
I6 See, for example, Sinn (1983).
” See Markowitz (1970).
B. Nook-boom / Diffusion, uncertainty and firm sire
difference matters in the case of a skew distribution of returns.
A more fundamental point is whether it is
warranted to assume a trade off between expected returns and risk in terms of a ‘subjective price of risk’, yielding a deterministic
choice. What is the nature of this price? Generally, in mainstream economic theory, price
is the outcome of supply and demand, and
thereby functions as an objective signalling
device to producers and consumers, without
any need for subjective assessments of value.
In the present context of risk evaluation, is
there some kind of internal, intrasubjective
market determining the price of uncertainty?
There may well be a process of deliberation
or bargaining, within the organisation, with
different attitudes to risk acceptance among
different stakeholders, but it is doubtful that
this can be represented as an efficient market
which yields a stable price of risk which is
independent from the investment opportunities considered. A similar objection applies to
the use of Von Neumann-Morgenstern utility, whereby it is not expected net present
value that is maximized, but expected utility,
where the probabilities of outcomes are
weighted with utilities attached to them, and
then aggregated. Is it reasonable, i.e., behaviorally plausible or realistic, to assume such
utility weights as available prior to the decision? Even if experiments show that decision
makers, when pressed in an artificial decision
environment to choose among options of
varying risk, ‘reveal’ utility weights or indifference curves, this does not demonstrate that
they implicitly use such constructs in real
decision making. A utility function which is
zero for all outcomes below a survival value
and unity above that, would yield maximization of the probability of survival, where expected returns are ignored. The point we are
trying to make is that decision makers look at
both expected returns and risk of failure,
without knowing how to merge them into a
single measure of merit. Perhaps the two di-
115
mensions of the decision cannot be merged so
easily. Perhaps they are incommensurable,
with the result that the decision-maker vacillates between them, whereby the decision itself becomes probabilistic, with the balance
tipped perhaps, by Keynesian ‘animal spirits’,
internal bargaining or accidental circumstance. This would certainly make the obvious effects of ‘animal spirits’, advertising,
personal relations, power structures, confidence, service, image, etc. easier to understand.
In the established framework of deterministic trade-offs between expected returns and
risk, these effects remain a mystery, or are
ascribed to ‘irrationalities’ with which economic science has no business.” More in the
vein of the ‘behavioral theory’ programme I9
in economics, as explored by Simon (1957),
Cyert and March (1963), Leibenstein (1976),
Nelson and Winter (1974, 1982) and others,
we propose a probabilistic decision situation,
in terms of a gambling model of the adoption
of innovations. The term ‘gambling model’ is
not intended to suggest that entrepreneurs
undertake risky investments purely for the joy
of gambling (though that may be part of it),
but to indicate that they consider the decision
a gamble, lack a clearly defined price of risk,
vacillate between expected returns and risk,
and arrive at a decision by internal deliberation and bargaining to such an extent, that
the decision comes to resemble the rolling of
dice loaded by expected return and risk.
I8 As argued by Weintraub (1985a, b) the standard approach
in economics, labelled the ‘neo-Walrasian’ programme by
Weintraub, can be seen as a ‘research programme’ in the
sense of Lakatos (1970, 1978). As such it has a ‘core’ (rules
for constructing theories, which are shielded off from refutation) which contains the assumption that economic agents
optimize some objective function subject to constraints, a
‘positive heuristic’ with the injunction to construct theories
in which agents optimize, and a ‘negative heuristic’ with the
extradition of ‘irrational behavior’ and the injunction ‘to
keep sociology at bay’.
I9 It has not been and perhaps cannot be established, that it
can be considered a research programme in the Lakatosian
sense.
B. Nooteboom
116
/ Diffusslon,
In the internal process of deliberation or
bargaining, production managers and perhaps
also marketing managers may focus on the
expected rewards of installing a process innovation (lower costs, higher quality), while
financial managers may focus on financial
risks and workers may focus on the risks of
changing operating conditions. The present
approach is consonant with learning theory as
applied to decision making.20 According to
this perspective decisions more generally are
probabilistic as a result of perceived risk. As
experience or knowledge accrues, perceived
risk is reduced and the decision becomes more
deterministic.
4. A gambling model
The basic hypothesis which is maintained
(not directly subjected to falsification) is as
follows:
- The decision to adopt the innovation at
time t or to maintain it, if it was already
adopted in the past, is proportional to expected net benefits in the future.
- The decision not to adopt at time t or to
disadopt (scrap), in case of adoption in the
past, is proportional to the probability of
failure, defined as the probability that net
benefits are negative.
Of course, for a given firm the two probabilities should sum to unity.
This yields
E
‘= E+p.pf’
(2)
where
p = probability of ownership,
E = expected net present value of returns
WV),
pf = probability of failure, i.e., of negative
NPV,
*’ Cf. Wiswede (1985).
uncertainty and
firm
size
p = a parameter expressing the weight attached to risk pf relative to expected
returns E. p also includes a scaling coefficient depending on the unit of meas u r e m e n t o f E ($, g u i l d e r s , 1 0 0 0
guilders, . _. ).
This basic model may be the start of an
on-going research effort to develop models of
increasing sophistication. There are many
ways of specifying the stream of costs and
benefits over time, with associated probability
density
functions, and with possible differences between firms who have already
adopted and those who have not.
In particular, the following questions arise:
- What, if any, is the ‘vintage effect’: if
adoption takes place at time t, what are the
real effects on the costs/benefits of that
vintage of the innovation, from technological progress and accumulated learning after
t?
- What determines the perceptions of decision makers (or influencers in the decision
process) : present technology and present
potential of the firm (extrapolation of current conditions); all the available, limited
knowledge concerning future conditions
(rational expectations); full knowledge of
future conditions as they will actually be
(clairvoyance)?
Only in the case of clairvoyance would
there be no need for probability density functions (no risk), and would the decision be
based on a balance of certain costs and benefits (in present value terms). The most realistic assumption would probably be that
perceptions of future costs and benefits are
based on: characteristics of decision maker(s),
own experience in case of adoption in the
past, and partial incorporation of external
knowledge and experience (also depending on
characteristics of decision maker(s)). Assumptions have to be made as intermediate hypotheses, in order to arrive at the end result
of a model of ownership as a function of firm
B. Nooteboom / Diffusion, uncertainty and firm size
size. One can now choose from the following
approaches:
Direct testing. Form alternative intermediate hypotheses; test them directly on relevant data; pick the hypothesis that yields the
best empirical performance; use this to develop the model of ownership (which can
then in turn be tested empirically).
Indirect testing. Conduct a mathematical
study of the implications of different intermediate hypotheses for the specification of
(alternative) models of ownership, and test
the latter on relevant data. In this way the
intermediate hypotheses are tested only indirectly. Different intermediate hypotheses may
yield the same model of ownership, with different interpretations of the parameters.
Pragmatic approach. Go directly to the
specification of the simplest possible model of
ownership that still has sufficient plausibility
on the level of intermediate assumptions, and
test this against an alternative that is somewhat less restrictive on the level of intermediate assumptions. Depending on the results and on the interest in refinements of the
model, consider more sophisticated assumptions on the intermediate level.
The present article reports the results of
the third (‘pragmatic’) approach. The main
reason for taking this approach was that it is
the shortest one, and insights were required at
short notice for the purpose of policy formation. More sophisticated models are currently
under consideration.
To arrive at the simplest possible model,
the present assumptions are as follows:
(1) Each firm faces a probability distribution (density function) of future net returns, in present value terms, per unit of firm
size S (S is measured in number of people
involved or volume of output).
(2) This distribution of returns per unit of
firm size does not depend on firm size. This
implies: no economies or diseconomies of
scale; no dependence on firm size of perceptions of costs and benefits; no dependence on
117
firm size of the discount rate used for present
value calculations.
(3) The distribution does not depend on
whether or not the firm adopted the innovation in the past. This implies that there is no
learning or other benefit from past adoption
other than that incorporated in expectations
shared by all possible users (in the sample of
firms studied): previous adopters have no advantage. It also implies that current technology can be fully incorporated in previous
vintages of the innovation: previous adopters
have no disadvantage.
(4) The weight attached to risk of failure
relative to expected returns (parameter p in
(2)) does not depend on firm size.
Clearly, these assumptions are very restrictive, and call for discussion.
Assumption (1). This assumption by itself
does not seem problematic.
Assumption (2). Smaller firms are expected
to be less knowledgeable about opportunities
and risks than larger firms. As a result they
may be more pessimistic or on the contrary
more optimistic, so that a priori the impact
on adoption decisions is not clear. Economies
or diseconomies of scale may occur, but again
it is a priori not clear which is the case.
In the case of (general purpose) computers,
for example, implementation may be relatively more costly in larger organisations due
to the larger number of people or hierarchical
levels of organisation involved, yielding more
complex and lengthy communications, deliberation and procedures. On the other hand,
it may be cheaper and faster due to a higher
level of education/training and the availability of more specialized expertise. Smaller firms
are expected to be less oriented towards the
longer term, and thus to employ (implicitly or
consciously) a higher discount rate.
Assumption (3). Past adopters may face
other future streams of costs and benefits
than non-adopters, and this may depend on
how long ago adoption took place. A priori, it
is hard to say what the balance of ad.
118
B. Nooteboom / Diffusion, uncertainty and firm size
vantages/disadvantages or earlier adopters is.
For example, consider the case of (general
purpose) computers. On the one hand, past
experience will yield improved prospects for
future returns: people are trained and have
experience; computer programmes have been
debugged; new applications may have been
developed in house; new and better outside
software may be implementable. On the other
hand, new applications may not be implementable, due to incompatability with older
systems, or may involve a change of knowledge/experience which is more costly than
starting from scratch.
Assumption (4). Smaller firms may be systematically less risk averse than larger firms,
but the reverse may also be true. Small business is often divided into two groups: technology driven, risk seeking firms and more
conservative, passive followers. The first type
is expected to be less risk averse than large
business, and the second type is expected to
be more risk averse than large business. On
this score, there are also correlations with the
age of the entrepreneur, his educational level
and age of the firm. Therefore, the influence
of firm size will depend on the composition of
the sample studied. The attitude towards the
risk of employing the innovation will also
depend on the penalty attached to its failure
relative to the total size of the firm’s operations, and the correlation of that risk with
the risks involved in other activities of the
firm. In this respect, one would in general
expect larger firms to be less risk-averse, due
to a larger size of operations combined with a
greater spread (less correlation) of risks.
However, in the case of general purpose computers, it seems reasonable to assume that
adoption pervades all activities of the firm.
That is also why we assume costs and benefits
to be proportional to firm size.
These issues should ideally be subjected,
one by one, to empirical research. Since a
priori it is not clear in which directions factors will operate, and in what way, we start
with the hypothesis that they do not occur or
cancel out, in order to arrive at the simplest
possible model that may apply. This model
will be tested empirically against a more general model that allows for a more complex
effect of firm size (since that is the effect we
are most eager to study). In the present study,
only a very limited attempt will be made to
model the change of parameters in time, and
no attempt is made to model differences between new and past adopters.
Under the specified assumptions, expected
net returns are as follows:
E(S, t) = E(t)S
(3)
where
E( S, t) = expected net returns, in present
value, of a firm with size S, at time
e(t)
= expected net return per unit of firm
size, resulting from ownership at
time t.
The probability of failure was defined as the
probability that returns will be negative, which
equals the probability that expected net return per unit of size is negative. Since by
assumption the corresponding probability
density function is independent of size, we
have
(4
where
pf( S, t) = probability of failure, for a firm
with size S, at time t,
v(t)
= probability of negative net returns
per unit of firm size.
Substitution of (3) and (4) in (2) yields
PC% t> =
E(t) . s
S
E(t)*S+p*cp(t) = s+a(t)’
a(t) = vJJ(t)
E(t) ’
\
‘(5)
B. Nooteboom / Diffusion, unceriainty and firm size
where
p( S, t) = probability of ownership of a firm
with size S at time t.
Summing up, the model hinges on two sets
of assumptions:
- probability of ownership is proportional to
expected net returns and probability of
non-ownership is proportional to risk of
failure,
- expected returns from ownership are proportional to firm size and probability of
failure is independent of size.
This model will be tested against a more
general specification:
so
P(S, t)= P+a*(t)
’
(6)
5. Properties of the model
Model (5) implies that smaller firms are
slower to adopt than large firms. It further
implies
(7)
lim p(S, t) = 0,
lim p(S, t) = 1.
S-+rx,
s-+0
In other words: firms of zero size never
adopt, and as firm size (and hence available
funds) approaches infinity, adoption will be
certain. This seems reasonable. The model
further implies
ss
= i (1 -
p)‘,
so that
(La)2
lim Sp = 1
s-+om
a’
dt
<o
d2&) >
’
dt2
o
’
-- lim
I--‘00
a(t)
= 0.
(10)
This specification allows for dependence on
firm size of: expected net return per unit of
firm size (economy or diseconomy of scale),
risk aversity and risk of failure.
6P
-=
the further assumption that (Y will consistently decline in time, and will ultimately
reduce to zero, because technological progress
will increase expected returns, and the dispersion of the probability density of returns will
reduce, thus reducing risk, as the innovation
matures and its potential becomes settled,
well known and standard. What this says, of
course, is that the innovation becames less
and less innovative. It is also reasonable to
assume that the decline of (Y will level off, due
to decreasing returns of technological improvement and learning by doing. Thus, we
assume
da(t)
p# 1.
119
lim 2 = 0
s+* 6s
’
(8)
(9)
According to (5), (Y is proportional to risk
(probability that net returns per unit of firm
size are negative) and inversely proportional
to expected net returns per unit of firm size.
Given this specification (based on earlier simplifying assumptions) it is reasonable to make
This does not preclude that LY reaches zero
at some finite point in time rather than in
infinity. It follows from (9) that as (Y declines
in time, the curve of p in relation to S rises
ever more sharply from S = 0. The above
properties are illustrated in Fig. 2, where the
curve of p in relation to S is plotted for
different values of CX, which results from the
later empirical study of the diffusion of computers in Dutch retailing. Model (5) also implies
(11)
If (Y has a fixed percentage decline rate,
(11) shows that the increase of ownership
percentage, for a given firm size, is largest
when ownership is 50%. With a fixed decline
rate, (11) reduces to the differential equation
of the logistic equation (for each level of firm
size), 21 which has a point of inflection at 50%
diffusion.
21 The assumption of a fixed percentage decline of (Y (exponential decline) would imply lim r---m a I = cc, and hence
lim , _ _ ,( S, t) = 0. This would imply that there is always a
nonzero probability of adoption, no matter how far we go
back in time. But something that has always been available
can hardly be called an innovation.
B. Nooteboom / Diffusion, uncertainty and firm size
120
probability/percentage c,f ownership 1%)
firm size (persons engaged)
Fig. 2. Size-dependent ownership for independent Dutch retailers.
For the totality of all firm sizes, the expected percentage of ownership is
PO) = f?-+, &f(s) dS
0
= s Co
o s +1(t) f(s) dST
where p(t) is the expected percentage of
owners at time t, in a given sector (all firm
sizes), and f(S) is the density function of the
size distribution of firms. This diffusion curve
satisfies the following boundary condition:
lim jr = 1 (following from (7)).
03)
t-+03
In other words, ultimately all firms will
employ the innovation. The exact shape of
the diffusion curve depends on the shape of
the size distribution. So far, it has been implicitly assumed that the size distribution does
not change in time. This assumption can be
abandoned. The model offers a framework
for studying the effects of increase of scale,
concentration or deconcentration on the diffusion of technology. There may be several
causes of changes in size distribution, includ-
ing the size-dependent diffusion of technology itself. The earlier introduction of technology by larger firms may favour their competitive position or profitability relative to smaller
firms. But such a study of size distribution
and its interaction with technology is beyond
the scope of the present paper.
6. The data
The empirical part of the present study
involves:
- a formal test of the relationship between
ownership and firm size p(S),
- a more informal test of assumptions concerning the time path of ar( t).
The data were obtained from a telephonic
inquiry among 1000 independent retailers in
different types of trade in the Netherlands,
conducted in September 1984. The shopkeepers were asked whether they operated a
(general purpose) computer, when it was installed, or whether they had an any plans for
installing a computer before end 1985, if they
B. Nooteboom / Diffusion, uncertainty and firm site
did not already have a computer. The addresses for the inquiry were sampled from a
panel of 6000 independent retailers operated
by the Research Institute for Small and
Medium Sized Business in the Netherlands
(EIM). The sample was distributed and
weighted across different types of trade to be
representative of independent retailing in the
Netherlands.
The data on computer ownership were
grouped in cells according to size of staff
(number of people engaged, including the
shopkeeper and his family; in full-time equivalents).
As already indicated, there were data for
different points in time: plans for purchase
before end 1985, ownership in September
1984, and information whether, in case of
ownership, a computer was already owned in
1983, 1982 or 1979. There is a possibility to
segment the data for total retailing into classes
of different types of trade. Finer segmentation of course yields fewer observations per
class. For the purpose of testing and estimating our model, we chose to segment the total
sample into two subclasses: **
(a) the top seven types of trade in terms of
computer ownership, with a total of 271 firms
observed. These types of trade were, in the
order of average ownership: electrical goods,
clothing, books, shoes, sportswear, furnishing
and do-it-yourself goods.23
(b) the remainder of the total sample (705
firms observed).
” This choice was based on a rather intricate argument, The
cells of observation were re-arranged so as to equalize, as
much as possible, the variance of computer owners per cell.
The total sample was segmented in two classes in such a
manner, that they would yield equal numbers of cells, for
1984 and 1985, with equal variance in all cells.
23 the reader may be surprised not to find the general food
trade in this class. The reason is, that this type of trade has
its needs covered to a large extent, not by the general
purpose computer considered in this study, but by dedicated systems in the form of scanning, cashing on the basis
of Price Look-up systems, automated scales and portable
devices for taking stock and registering orders.
121
Table 1 yields all the relevant data for
these two classes and the total sample.
7. Tests and estimates of the effect of firm
size
The empirical tests and estimates ae based
on the fact that the model (5) is a transformation of the standard logistic model:
1
(14)
’ = 1 + exp( & + &x) ’
If we substitute x = log S, & = log (Y, and
p1 = -1, this transforms into our model (5).
With pi = -p, it transforms into the more
general specification (6). Tests and estimates
were made by means of a maximum likelihood procedure for logit models developed at
the “Stichting voor Economisch Onderzoek”
(Foundation for Economic Research) at the
University of Amsterdam, which yields standard errors and allows for restrictions on the
coefficients. For further details on underlying
theory and technique, see Cramer (1986). The
procedure’ was as follows:
- substitution of log S as the explanatory
variable;
- unrestricted estimates of PO (as an estimate
of log (Y, which is then transformed into an
estimate of (Y (2) and & (as an estimate of
p). This corresponds to the more general
version of our model (6);
- estimate of & under the restriction pi =
- 1. This corresponds to the simple model
(5) which we wish to test against the alternative (6). This yields an estimate of the
parameter (Y in the simple model (hi>.
The procedure is applied for different years
to the two sets of data discussed in the previous section (top seven trades and remaining
trades). The results are given in Table 2. In all
cases the estimates of the parameter (Y according to the restricted logit model (corresponding with out hypothesis (5)) are strongly significant, have the correct sign and decline
consistently in consecutive years, as expected.
122
B. Nooteboom / Diffusion, uncertainty and firm size
Table 1
The basic data, for the finest available grid of cells, where n = number of firms, k = number of firms with computer (end of year.
except 1984), s= average firm size in the cell (number of persons engaged)
(a) Total sample
Year
Size class (number of persons engated)
5
n:
1985 =
1984 b
1983
1982
1979
1977
0.1-0.9
l-l.9
2-2.9
3-3.9
4-4.9
5-6.9
l-9.9
10-19.9
> 20
Total
0.20
0
1.31
152
2.21
229
3.25
166
4.19
123
5.68
124
1.99
93
13.08
72
36.44
17
4.71
976
-
8
3
2
2
2
27
12
8
4
1
38
13
6
2
2
-
-
29
7
4
3
3
2
31
14
6
5
2
2
27
9
4
1
-
36
19
15
8
2
-
11
11
8
6
3
1
206
89
51
31
14
5
k
k
k
k
k
k
(b) The top seoen types of trade (electrical goods, clothing, books, shoes, sportsgoods, furnishing, do it yourself)
Size class
Year
0.1-0.9
l-l.9
2-2.9
3-3.9
4-4.9
5-6.9
7-9.9
10-19.9
> 20
Total
-
1.32
30
2.24
57
3.23
47
4.26
38
5.47
33
8.33
31
12.73
25
23.71
10
271
k
3
k
k
k
1
8
4
17
6
2
1
16
6
3
3
3
2
13
4
2
2
-
13
4
2
-
13
7
7
4
1
-
3:
n:
1985 =
1984 b
1983
1982
1979
1977
1
k
1
1
k
-
8
8
6
5
1
1
91
40
24
14
7
3
(c) Remaining types of trade
Year
Size class
5:
n:
1985 =
1984 b
1983
1982
1979
1977
k
k
k
k
k
k
0.1-0.9
l-l.9
2-2.9
3-3.9
4-4.9
5-6.9
7-9.9
10-19.9
120
Total
0.20
1
1.31
122
2.20
172
3.26
119
4.16
85
5.76
91
1.95
61
13.27
47
47.19
8
4.55
706
-
6
3
2
2
2
20
8
7
3
-
20
6
4
2
2
12
1
1
-
19
10
4
3
2
2
14
5
2
1
-
23
12
8
4
1
-
-
-
4
4
2
2
2
117
48
29
16
8
2
a 1985 based on plans registered in September 1984.
b 1984 observed in September.
The test of the simple model (5) against the
more general model (6) is a test of the hypothesis & = - 1.
A t-test on the estimates of PI, in the
unrestricted logit model, indicates that the
hypothesis is to be rejected only in one out of
the ten cases (at the 95% confidence level).
A comparison between the loglikelihoods
(log L) of the unrestricted and restricted logit
models shows that the likelihood declines only
little in going from the unrestricted to the
restricted model. The significance of this decline is tested with a likelihood ratio test, as
follows:
LR = 2(log L, - log L2),
where log L, refers to the unrestricted model
and log L, to the restricted’ model. LR is
&i-square distributed with one degree of freedom. LR is significantly different from zero
B. Nooteboom / Diffusion, uncertainty and
(95% confidence level) in only one of the ten
cases (the same case as indicated by the t-test).
LR can be summed across the ten cases,
yielding a value of 10.24 with ten degrees of
freedom, which is far from significant. The
estimates for the restricted model were also
made for all types of trade taken together, to
test whether the results were significantly less
likely than those for the two groups (top
seven and remaining trades) taken apart. The
conclusion was that the separation into the
two groups did indeed yield more likely results.
Fu
f i r m size
123
I
300
200
8. The time path of a
In Fig. 3, the estimates of cr (see Table 2)
are plotted against time, 24 to see whether
they conform to the expectations and hypotheses discussed in Section 5 (formula (10)).
The results appear to confirm t.he hypothesis
that (Y yields a monotone decline. The results
appear to contradict the hypothesis that the
second derivative of (Y is everywhere positive:
in relevant ranges the slope of the decline
appears to be fairly fixed. In other words the
decline is often more linear than curvilinear.
The hypothesis that the decline of (Y would
consistently level off was based on the assumption of diminishing returns of technological progress and learning by doing.
The results indicate that a zero value of (Y
is reached very closely, not in the very long
but in the fairly short term. In the case of the
top seven trades that point appears to be
reached in 1987 at the latest, and in the case
of the remaining trades a year or so later.
Within the framework of the model the results indicate that either for the increase of
expected returns or for the decline of uncertainty, or both, there are no diminishing re24 In contrast with the other years, the data point in 1984 is
located at 0.75 of the year, since it applies to an observation
in September.
100
I
I
79
I
I
82
I
83
I
84
I
85
Time
Fig. 3. Decline of &.
turns of technology and learning until (Y has
become quite small.
Table 3 shows that the percentage decline
of the estimates of CY increases in time. The
explanation of this faster than exponential
decline of (Y is a matter for further research.
9. Further research
Further research is planned to test and
estimate the model on a much wider sample
of data across all sectors of the Dutch economy. The formal results are not available yet,
but an impression is given in Figs. 4 and 5.
The figures give the degree of automation
(percentage of firms with a computer) in relation to firm size for the main sectors of the
B. Nooteboom / Diffusion, uncertainty and firm size
124
Table 2
Estimates of the logit model with and without restriction.”
Without restrictions
B
Restriction
1% L,
P4
B
/3, = - 1
log L,
LR
T o p sewn t r a d e s :
1979
1982
1983
1984
1985
139.60
(146.13)
285.37
(246.76)
266.19
(206.65)
38.57
(18.70)
8.71
-0.72
(0.54)
- 1.61
(0.38)
- 1.79b
(0.35)
-1.17
(0.25)
-1.00
(2.88)
(0.20)
332.19
(252.74)
158.74
(88.42)
76.36
(32.15)
67.13
(24.42)
18.39
(4.43)
-0.96
(0.37)
-0.92
(0.28)
-0.84
(0.22)
-1.07
(0.19)
-0.95
(0.14)
- 27.908
- 50.427
- 62.100
- 101.141
- 158.297
236.33
(98.37)
82.99
(21.81)
55.13
(12.34)
28.31
(5.04)
8.69
(1.18)
- 28.046
0.276
- 51.809
2.764
- 65.022
5.844b
- 101.388
0.494
- 158.297
-
Other trades:
1979
1982
1983
1984
1985
-45.261
- 75.348
- 117.488
- 162.629
- 294.921
a Standard errors between parentheses; LR is &i-square
b Significant deviation from the hypotheses PI = - 1
Table 3
Average percentage decline of IX (%).
Top seven trades
Remaining trades
19821983
19831984
19841985
30
20
34
46
59
50
61
59
- 45.265
0.008
- 75.389
0.082
- 117.732
0.488
- 162.696
0.134
- 294.994
0.146
distributed with one d.f.
Dutch economy in 1983 and 1985, on the
basis of data from the Dutch Central Bureau
of Statistics. For an estimate of the model,
attempts are under way to obtain the data for
a more detailed break down into more homogeneous sectors (subsectors of manufacturing;
separation of retailing, hotels/restaurants/
cafe’s and repairs; subsectors of business
services). At this stage, Figs. 4 and 5 are
19791982
355.29
(120.14)
183.38
(45.64)
99.90
(19.03)
59.54
(9.06)
19.99
(2.11)
a Account has been taken of the fact that the ibservation in
1984 took place in September, while the other observations
were made at the end of the year.
presented to show that the relation between
degree of automation and firm size appears to
be very much like the pattern predicted by
our present model (see Fig. 2). After further
tests of the model of the relation between
degree of automation and firm size, the
parameter (Y will be estimated per sector, for
different years, and further research will concentrate on explanations of the development
in time of (Y, and of its difference between
different sectors.
A complementary line of research would be
to investigate alternative specifications of the
model on the basis of a reevaluation of the
simplifying assumptions discussed in Section
4 of the present article. This yould probably
lead to more complex models, allowing for
more complex effects of firm size and additional explanatory variables and parameters
B. Nooteboom
/ Diffusion, uncertainty and firm size
100
______------ _ -. -. -. _._.L.-.-.
90
80
/’
70
/
60
/’
/
- - _.
-.,
___--- _ --,
___L---. ........ ...
.__.e--- __---. . . . . . . . . . . . . . . ,.s.......
. _. . . . . . . . . . . . . . .
/#
,’
50
40
3a
20
.:’
ia
0
20
40
60
80
100
120
140
160
180 2 0 0 220 2 4 0 260 280
30 IO
firm slzr 1" persons engaged
Fig. 4. Degree of automation (% of firms with a computer), 1983.
*
80
..
. ...
:.’
-c
. . ..
/.:* /.’ *I
:;*
!O
40
I30
80
extractlo"
*..* . . . . .
- - --^-.-.-.
100
17.0
- _ - - _ _ _ _ ._ ._ _ _ _ _ _
-.-_.-. -. . . . . . . . . . . . . . .- .-.___--- _--. . . .,...... . . . . . . . *-..
__-- --_--_-_---
140
160
200
220
240
& ma""fact"rl"g
bulldmg
wholesale
retail, hotels/rPstaurant/cafes,
business services
sounx: central
180
rrpalr*
Bureau of Statistic
Fig. 5. Degree of automation (% of firms with a computer), 1985.
260
280
3t
0
125
126
B. Nooreboom / Diffusion, uncertainty and firm size
(characteristics of potential adopters, market
structure, marketing mix variables of suppliers, etc.). It would probably also lead to
different decision models for new and old
adopters. A simple assumption concerning old
adopters would be that there is no way back:
once an innovation is adopted, it is maintained. A more sophisticated approach would
be to take into account the scrap value and
productivity of older vintages of the innovation compared to current costs and state of
the art. In this way the model would expand
into a model of both new purchases and
replacement purchases.
This might well be of interest to suppliers
of computers or software. Another line of
research would be to apply the ideas and
methodology for the development of diffusion models for other innovations where the
effect of firm size is considered to be important.
10. Practical implications
In contrast with David’s model, discussed
in Section 2, the present model does not hinge
on the ‘Lumpiness’ of the investment. This is
an advantage. In the case of (general-purpose) computers, for example, computing
facilities can now be purchased at very low
size and cost (microcomputers). In contrast
with Davies’ model, the model does not hinge
on the independence of many firm characteristics related to pay-back period. In contrast
with both David’s and Davies’ models, the
model does not look only at expected costs
and benefits, but also at uncertainty.
There are practical implications on two
levels: technology policy and industrial
marketing. Relevant decision makers in technology policy are government agencies, advisory bodies, associations of entrepreneurs,
trade organizations, etc. In industrial marketing one might think of producers and distributors of innovations for business (e.g., com-
puters), and associated business services (in
the case of computers: software houses, automation consultants).
In the area of technology policy, the model
was used to answer two questions that were
urgent at the time (1985):
- To what extent is the lag of small business
in the adoption of computers an indication
of weak management that requires action
on the part of policy makers and advisory
bodies?
- What are the implications of the widening
lag in adoption between small and large
business, that was observed in 1984, and
what pattern of diffusion can be expected
for the future?
On the basis of the present study, the
answers were as follows:
- It is rational for entrepreneurs to make a
trade-off between expected returns and risk.
On the (reasonable) assumption that expected returns are proportional to size and
risk is independent of size, it is only to be
expected that small firms will lag behind
(i.e., this has a rational basis).
- Due to the S-curve properties of the diffusion curve, it is to be expected that the gap
between large and small businesses widens
at first. Later (our prediction, in the case of
retailing, was around 1986), the gap would
start to close very fast.
- If government or associated institutions for
advice and counselling to small business
were to make policy and undertake action,
it should be directed not at pressing entrepreneurs to install computers, but at reducing perceived risk by means of realistic
and accessible information on costs and
benefits, and on improving expected benefits by stimulating applications (systems
and software) relevant for small firms.
For industrial marketers, the practical implications are as follows:
- The model may be used ‘as an aid for
planning by predicting market demand, and
for segmentation by indicating in what seg-
B. Nooteboom / Diffusion, uncertainty and
ments of firm size growth is to be expected
in the near and in the further future.
- The model demonstrates that in determining the allocation of funds for improved
market position, a trade-off should be made
between improving performance (shifting
the probability density of costs and benefits to higher levels of net returns) and
reducing perceived risk (narrowing the dispersion of the probability density at a given
level of performance). The latter may be
sought in improved reliability (as opposed
to level) of performance, more reliable and
accessible communication of possible applications and associated costs and benefits, and more implementation support,
training of users, demonstrations, manuals,
guarantees of performance or buy-back
guarantees in case of failing applications.
It is not only improved performance but
also reduced risk that can offer competitive
advantage.
The model might also be used to differentiate prospective sales in different segments
between competing suppliers, and may be
extended to include marketing mix variables.
This could yield a more systematic trade-off
between quality, price, distribution, service
and communication, as a refinement of the
trade-off between costs/benefits and risk reduction.
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